9.36 Summary of Key Duration and Convexity Relationships
Regarding Yield
- We (long ago) demonstrated the relationship between yield and price, based on TVM.
- We demonstrated earlier herein the relationship between yield and duration.
- Duration and Convexity are positively related because one is arrived at by multiplying the present value of the cash flows by “p,” while is other is multiplied by “p (p + 1),” a.k.a. “p2 + p.”
| If Coupon | Decreases | Then… | Dollar Price | Decreases |
| Duration | Increases | |||
| Convexity |
| If Yield-to-Maturity | Decreases | Then… | Dollar Price | Increases |
| Duration | ||||
| Convexity |
Regarding Coupon
- Again, think of the zero-coupon bond as your base case; a Zero has the lowest dollar price of all; its discount is greatest. Therefore, if the coupon goes down, the price is discounted more, the price goes down. If the coupon goes up, the price goes up, and (ALCF and) Duration and Convexity go down.
- If price goes down – as in our base Zero case, (ALCF and) Duration and Convexity must go up. Zeroes – with its lowest prices – have the greatest Duration and are the most Convex, the most volatile.
